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The structure of \(\ell\)-group varieties. (English) Zbl 0439.06013

MSC:
06F15 Ordered groups
06B20 Varieties of lattices
08B15 Lattices of varieties
08B25 Products, amalgamated products, and other kinds of limits and colimits
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[1] S. J. Bernau, Varieties of lattice groups are closed under-completion, Symposia Math. XXI (1977), 349–355. · Zbl 0374.06010
[2] C. G. Chehata,An algebraically simple ordered group, Proc. London Math. Soc.,2 (1952), 183–197. · Zbl 0046.02501
[3] A. H. Clifford,A noncommutative ordinally simple ordered group, Proc. American Math. Soc.,2 (1952), 902–903. · Zbl 0044.01301
[4] P. F. Conrad, Lattice Ordered Groups, Lecture notes, Tulane University, 1970. · Zbl 0258.06011
[5] A. M. W. Glass, Ordered Permutation Groups, Bowling Green State University, 1976. · Zbl 0352.06010
[6] W. C. Holland,The lattice-ordered group of automorphisms of an ordered set, Michigan Math. J.,10 (1963), 399–408. · Zbl 0116.02102
[7] W. C. Holland,The largest proper variety of lattice-ordered groups, Proc. American Math. Soc.,57 (1976), 25–28. · Zbl 0339.06011
[8] W. C. Holland,Varieties of -groups are torsion classes (to appear). · Zbl 0432.06011
[9] W. C. Holland andJ. Martinez,Accessibility of torsion classs (to appear). · Zbl 0428.06011
[10] W. C. Holland andS. H. McCleary,Wreath products of ordered permutation groups, Pacific J. Math.,31 (1969), 703–716. · Zbl 0206.31804
[11] J. Martinez,Free products in varieties of lattice-ordered groups, Czech Math. J.,22 (1972), 535–553. · Zbl 0247.06022
[12] J. Martinez,Archimedean-like classes of lattice-ordered groups, Trans. American Math. Soc.,186 (1973), 33–49. · Zbl 0298.06022
[13] J. Martinez,Varieties of lattice-ordered groups, Math. Z.,137 (1974), 265–284. · Zbl 0281.20023
[14] J. Martinez,Torsion theory for lattice-ordered groups, Czech. Math. J.,25 (1975), 284–299. · Zbl 0321.06020
[15] S. H. McCleary,Closed subgroups of lattice-ordered permutation groups, Trans. American Math. Soc.,173 (1972), 303–314. · Zbl 0327.06012
[16] H. Neumann,Varieties of Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, #37, Springer Verlag, New York, 1967. · Zbl 0149.26704
[17] Alexander Pope, Windsor Forest, 1713 (lines 13–16).
[18] J. A. Read,Wreath products of non-overlapping lattice-ordered groups, Canadian Math. Bull.,17 (1975), 713–722. · Zbl 0313.06012
[19] E. B. Scrimger,A large class of small varieties of lattice-ordered groups, Proc. American Math. Soc.,51 (1975), 301–306. · Zbl 0312.06010
[20] J. E. H. Smith,The Lattice of -group Varieties, Ph.D. thesis, Bowling Green State University, 1976.
[21] M. R. Vaughn-Lee,Uncountably many varieties of groups, Bull. London Math. Soc.,2 (1970), 280–286. · Zbl 0216.08401
[22] E. C. Weinberg,Free lattice-ordered abelian groups, Math. Ann.151 (1963), 187–199. · Zbl 0114.25801
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